Solution
= Solution
\b[True.] If $|f(x_0)|\gt C$, continuity gives an interval of positive length on which $|f|\gt C+\delta$. Its $L^p$ norm exceeds $(C+\delta)\ell^{1/p}$, which tends to $C+\delta\gt C$ as $p\to\infty$, a contradiction.
= Solution
\b[True.] If $|f(x_0)|\gt C$, continuity gives an interval of positive length on which $|f|\gt C+\delta$. Its $L^p$ norm exceeds $(C+\delta)\ell^{1/p}$, which tends to $C+\delta\gt C$ as $p\to\infty$, a contradiction.